using OrdinaryDiffEqSSPRK
using Trixi

###############################################################################
# semidiscretization of the compressible Euler equations

equations = CompressibleEulerEquations2D(1.4)

"""
    initial_condition_double_mach_reflection(x, t, equations::CompressibleEulerEquations2D)

Compressible Euler setup for a double Mach reflection problem.
Involves strong shock interactions as well as steady / unsteady flow structures.
Also exercises special boundary conditions along the bottom of the domain that is a mixture of
Dirichlet and slip wall.
See Section IV c on the paper below for details.

- Paul Woodward and Phillip Colella (1984)
  The Numerical Simulation of Two-Dimensional Fluid Flows with Strong Shocks.
  [DOI: 10.1016/0021-9991(84)90142-6](https://doi.org/10.1016/0021-9991(84)90142-6)
"""
@inline function initial_condition_double_mach_reflection(x, t,
                                                          equations::CompressibleEulerEquations2D)
    if x[1] < 1 / 6 + (x[2] + 20 * t) / sqrt(3)
        phi = pi / 6
        sin_phi, cos_phi = sincos(phi)

        rho = 8.0
        v1 = 8.25 * cos_phi
        v2 = -8.25 * sin_phi
        p = 116.5
    else
        rho = 1.4
        v1 = 0.0
        v2 = 0.0
        p = 1.0
    end

    prim = SVector(rho, v1, v2, p)
    return prim2cons(prim, equations)
end

initial_condition = initial_condition_double_mach_reflection

boundary_condition_inflow = BoundaryConditionDirichlet(initial_condition_double_mach_reflection)

# Supersonic outflow boundary condition. Solution is taken entirely from the internal state.
# See `examples/p4est_2d_dgsem/elixir_euler_forward_step_amr.jl` for complete documentation.
@inline function boundary_condition_outflow(u_inner, normal_direction::AbstractVector, x, t,
                                            surface_flux_function,
                                            equations::CompressibleEulerEquations2D)
    # NOTE: Only for the supersonic outflow is this strategy valid
    # Calculate the boundary flux entirely from the internal solution state
    return flux(u_inner, normal_direction, equations)
end

# Special mixed boundary condition type for the :Bottom of the domain.
# It is Dirichlet when x < 1/6 and a slip wall when x >= 1/6
@inline function boundary_condition_mixed_dirichlet_wall(u_inner,
                                                         normal_direction::AbstractVector,
                                                         x, t, surface_flux_function,
                                                         equations::CompressibleEulerEquations2D)
    if x[1] < 1 / 6
        # From the BoundaryConditionDirichlet
        # get the external value of the solution
        u_boundary = initial_condition_double_mach_reflection(x, t, equations)
        # Calculate boundary flux
        flux = surface_flux_function(u_inner, u_boundary, normal_direction, equations)
    else # x[1] >= 1 / 6
        # Use the free slip wall BC otherwise
        flux = boundary_condition_slip_wall(u_inner, normal_direction, x, t,
                                            surface_flux_function, equations)
    end

    return flux
end

boundary_conditions = (; Bottom = boundary_condition_mixed_dirichlet_wall,
                       Top = boundary_condition_inflow,
                       Right = boundary_condition_outflow,
                       Left = boundary_condition_inflow)

volume_flux = flux_ranocha
# Up to version 0.13.0, `max_abs_speed_naive` was used as the default wave speed estimate of
# `const flux_lax_friedrichs = FluxLaxFriedrichs(), i.e., `FluxLaxFriedrichs(max_abs_speed = max_abs_speed_naive)`.
# In the `StepsizeCallback`, though, the less diffusive `max_abs_speeds` is employed which is consistent with `max_abs_speed`.
# Thus, we exchanged in PR#2458 the default wave speed used in the LLF flux to `max_abs_speed`.
# To ensure that every example still runs we specify explicitly `FluxLaxFriedrichs(max_abs_speed_naive)`.
# We remark, however, that the now default `max_abs_speed` is in general recommended due to compliance with the
# `StepsizeCallback` (CFL-Condition) and less diffusion.
surface_flux = FluxLaxFriedrichs(max_abs_speed_naive)

polydeg = 4
basis = LobattoLegendreBasis(polydeg)
shock_indicator = IndicatorHennemannGassner(equations, basis,
                                            alpha_max = 0.5,
                                            alpha_min = 0.001,
                                            alpha_smooth = true,
                                            variable = density_pressure)
volume_integral = VolumeIntegralShockCapturingHG(shock_indicator;
                                                 volume_flux_dg = volume_flux,
                                                 volume_flux_fv = surface_flux)
solver = DGSEM(polydeg = polydeg, surface_flux = surface_flux,
               volume_integral = volume_integral)

# Get the unstructured quad mesh from a file (downloads the file if not available locally)
mesh_file = Trixi.download("https://gist.githubusercontent.com/andrewwinters5000/a0806ef0d03cf5ea221af523167b6e32/raw/61ed0eb017eb432d996ed119a52fb041fe363e8c/abaqus_double_mach.inp",
                           joinpath(@__DIR__, "abaqus_double_mach.inp"))

mesh = P4estMesh{2}(mesh_file)

semi = SemidiscretizationHyperbolic(mesh, equations, initial_condition, solver;
                                    boundary_conditions = boundary_conditions)

###############################################################################
# ODE solvers, callbacks etc.

tspan = (0.0, 0.2)
ode = semidiscretize(semi, tspan)

summary_callback = SummaryCallback()

analysis_interval = 100
analysis_callback = AnalysisCallback(semi, interval = analysis_interval,
                                     extra_analysis_integrals = (entropy,))

alive_callback = AliveCallback(analysis_interval = analysis_interval)

save_solution = SaveSolutionCallback(interval = 100,
                                     save_initial_solution = true,
                                     save_final_solution = true,
                                     solution_variables = cons2prim)

# positivity limiter necessary for this example with strong shocks
positivity_limiter = PositivityPreservingLimiterZhangShu(thresholds = (5.0e-6, 5.0e-6),
                                                         variables = (Trixi.density,
                                                                      pressure))

amr_indicator = IndicatorLöhner(semi, variable = Trixi.density)

amr_controller = ControllerThreeLevel(semi, amr_indicator,
                                      base_level = 0,
                                      med_level = 3, med_threshold = 0.05,
                                      max_level = 6, max_threshold = 0.1)

# Set `limiter! = positivity_limiter` to apply the positivity-preserving limiter after 
# coarsening and refinement steps.
amr_callback = AMRCallback(semi, amr_controller,
                           interval = 1,
                           adapt_initial_condition = true,
                           adapt_initial_condition_only_refine = true,
                           limiter! = positivity_limiter)

callbacks = CallbackSet(summary_callback,
                        analysis_callback, alive_callback,
                        save_solution,
                        amr_callback)

###############################################################################
# run the simulation
sol = solve(ode, SSPRK43(; stage_limiter! = positivity_limiter);
            ode_default_options()..., callback = callbacks);
